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Thursday, April 03, 2008

Black Holes at the LHC - What can happen?

Black holes sound like dangerous beasts, evoking voracious vacuum cleaners that suck in everything in their neighbourhood. If they are created at the LHC, that may mean the end of the world - or so one might think, with an intuition gained mainly from the exposure to special effects of science fiction movies.

The reality is more prosaic.

First of all, mini black holes at the LHC are an option only if one of the theories of "large extra dimensions" was in fact true. But of course, these theories are only speculations so far. Second, should mini black holes be created in high-energy particle collisions, they would evaporate very fast, due to Hawking radiation. Though Hawking radiation has not been experimentally verified so far, its existence is expected in almost all theoretical scenarios investigated (no matter where you go, you will always find somebody who disagrees on something).

But what would happen in the (quite unrealistic) case that tiny black holes were created at the LHC, and that they did not decay by the emission of Hawking radiation?

It's important to keep in mind that black holes do not have some special "vacuum cleaner" property - they just attract other stuff by the force of gravity.

Now, the tiny black holes that could be created at the LHC if theories of large extra dimensions were indeed correct would have masses in the range of a few TeV. 1 TeV corresponds to about 1000 times the mass of a proton, which is 0.94 GeV, or 1.7×10-27 kg. The corresponding Schwarzschild radius is about 1/1000 fm, or 10-18 m.

Because gravity is such a weak force, it's safe to assume that nothing happens to matter that encounters the black hole at a larger radial distance than one Schwarzschild radius. Assuming for simplicity that all stuff hitting with a smaller distance gets sucked in, the black hole has a cross section of about 10-36 m², or 10 nanobarn (that's more than typical neutrino cross sections).

What happens if such a "naive" black hole passes through the Earth?

For simplicity, we can assume that the Earth is made up of iron, with a density of 8 g/cm³, or 8000 kg/m³. Since mass is essentially the mass of nucleons (the protons and neutrons in the nuclei of the atoms), and taking into account the proton mass, this density corresponds to a density of 5×1030 nucleons per m3. But this means that on average, the black hole would travel 200 km before encountering a nucleon (200 km travel distance × 10-36 m² cross section × density of nucleons of 5×1030 nucleons per m3 equals one nucleon).

Nobody knows exactly what will happen when a tiny black hole hits a nucleon. On the scale of the black hole, the nucleon is about 1000 times larger in diameter, and a very dilute cloud of a few quarks and gluons. It may be that the black hole hits one of these partons, as they are called, thus disrupting the nucleon and carrying away a fraction of its mass. There is no theory to describe this, and there are all kinds of problems involved, as to what happens to confinement, colour neutrality, and so on. But whatever happened, in the end, the black hole may have gained, in the most extreme case, the mass of a nucleon.

Now, this is just one permille of the mass of the black hole, so it won't change its momentum, and just travel on along a straight path. After 100 encounters or so with nucleons, on average, it will have left the Earth, even if goes right through its centre. In addition one should keep in mind that scenarios in which a black hole can reach a thermodynamically stable endstate (though these scenarios are strongly disfavored for theoretical reasons), once the black hole would gain some mass it would no longer be in this stable endstate, and evaporate again until it reaches again its initial mass.

If the black hole starts at rest on the Earth's surface, it will fall through the centre of the Earth and engage in the oscillatory motion that is set as a problem in undergraduate textbooks, dealing with the free fall through a tunnel across the Earth.

But does the black hole start at rest, in the first place?

In fact, if the initial velocity of the black hole is larger than the escape velocity of the Earth's gravitational field, it will just escape into space. The escape velocity for the black hole is 11.2 km/s, the same as for any ordinary canon ball or satellite. This corresponds to a value of β = v/c ≈ 0.00004. That's tiny for typical high-energy collision kinematics, and most black holes produced will easily exceed this number by orders of magnitude. Earth' gravity can not trap these black holes created in the collision.

Even though the centre of mass frame of the colliding protons at the LCH is at rest with respect to the detectors and the surface of the Earth, this is generally not the case for the pair of colliding partons that creates the black hole. As a consequence, the black holes will have quite large momenta along the beam axis. Technically speaking, this momentum is expressed by a variable called rapidityy, where y = arctanh β. The black hole can become trapped in the Earth's gravitational field only unless its rapidity exceeds 0.00004 (for such a small argument, arctanhβ is pretty much the same as β).

Now, here is a plot of the rapidity distribution of black holes from collisions at the LHC, assuming large extra dimensions.

Although this is not the initial rapidity distribution of the nascent mini black holes, the essential feature of the plot is clear: the typical rapidity of the black holes is of the order 1. For comparison, the rapidity of the 7 TeV colliding protons is 9.6. This means that just about one in 100000 tiny black holes produced will have a velocity along the beam axis smaller than escape velocity. But even these black holes will have some initial velocity in the direction perpendicular to the beam axis. This velocity is usually expressed by the "transverse momentum", and typically, it is also much bigger than the escape velocity. There are no tiny black holes created "at rest" in the detector!

In short: If tiny black holes were produced because large extra dimensions did exist in the necessary number with the necessary radius, and if they did not evaporate within 10-26 seconds as expected (Hawking evaporation is considered a very robust prediction, so this scenario is not confirmed by well founded theories), most of them would have such a high velocity that they escaped the gravitational field of the Earth for good. Even if they travelled straight through the centre of the Earth, the few nucleons they can hit wouldn't change their momentum in an appreciable way.

80 comments:

changcho
said...

Nice summary of this 'black-hole creation at the LHC' problem we've been hearing so much about, lately. This is also the first I hear about the speed distribution of the putative mini black holes, such that most would escape Earth.

Angular momentum is conserved. Anything macroscopic swirling into a 2x10^(-9) nanometer diameter drain hole will spin about like the dickens but not go in.

L = mvr

A kid's marble swirling into a hole 10^16 times smaller will speed up 10^16 times. Human brisk walking speed is 3 mph or 134 cm/sec. a marble is grabbed by a black hole with an initial swirl velocity of 1 cm/sec (very slow). Near the event horizon it is moving at "10^16 cm/sec." The mini-black hole will not rapidly swallow matter. Anything nearby will be violently repelled by radiation emission of what little has been trapped.

Hi Stefan!Thanks for this post.Although Greg Landsberg might have said it before you, he obviously chose some very different cross-section as his mini-black-hole scattering rate is <1 in an iron block the size of the earth-moon distance...

By the way: If the LHC produces black holes at all, optimistic predictions claim their production rate to be about one per second, so the tiny fraction of black holes that don't escape from earth might matter as well. What happens with them if there is no Hawking radiation?

The story you've told is all well and good, but technically it isn't enough to be reassuring by itself, especially not if you're trying to set extraordinarily strong limits on an extraordinarily bad thing like the entire earth being eaten. As noted above, it is imaginable that the LHC will produce a lot of black holes.

I went to a talk by Michelangelo Mangano in Berkeley last week, and he and his colleagues in the Safety Assessment Group have done a lot of detailed work tying up loose ends. Their arguments are more than convincing, even if one requires an extremely high margin of error and ignores the improbability of stable black holes entirely — but I think it's worth noting that the "small phase space for black holes below escape velocity" argument isn't quite enough on its own.

I agree with you. It wasn't the intention of this post to come up with all the reasons that have been repeated a thousand times. This post developed out of a discussion from the previous post, and it doesn't even attempt to describe a remotely realistic scenario (as repeated various times, it assumes the black holes don't evaporate, which is a strongly disfavoured by theory). Best,

A question which fascinates me, and hopefully it is sufficiently on-topic, is what is the size and population distribution of black holes throughout the universe.

The question involves theory, experiment and observation. It involves the early characteristics of the big bang, it involves considering what processes could be involved in the formation and evaporation of black holes.

We can ask, what is implied by the fact that we can look up into the sky (or beneath our feet) and see things other than black holes.

At the moment it seems that there are two basic sizes for black holes that actually exist, namely stellar black holes and galactic black holes. But why aren't there black holes of all other sizes (or are there)?

Also, more directly on-topic, what is the effect of mini black holes having charge (or color) for the consideration in the Original Post.

A great post, that I found both interesting and informative. It nice to see how rare an event it would to be to have a mini black hole, that is only remotely possible to form, which is highly unlikely to last long enough to even count to have ever existed, to finally have a momentum small enough to even stay within the bounds of the earth. However, more to address Seth’s comment then your intent, is to realize this is all just preaching to the choir, so to speak.

I think it’s safe to say that almost anyone that has a reasonable understanding never did have any worries attached to the LHC; that is in terms of it posing any kind of real danger. Despite what Seth might think, there isn’t a degree of explanation that will convince and assure people whose true problem rests solely with their own irrational fear. Like I said over on another blog a few weeks ago; it’s an old clique that the future belongs to the brave. However, this is not true, for it has always simply belonged to the inspired, rationally confident, educated and informed. It would serve the others right if we left them behind. However, this also is not an option, as many are our friends and relatives. So as usual, they will have to go as they often do, kicking and screaming :-)

I don't have anything to say on the post which is probably right about black holes, however I see that most people apply some very closed minded thinking to the "problem". I just want to show my point of view many seem not to consider. Please bear the provocative form of this post.

The LHC is an experience done for the first time in history, using huge financial and technical capabilities. Many say the produced phenomenon is already happening naturally in the universe and that it means there is no risk. But more objectively we can say it doesn't imply any safety as there is two key differences here : The distance to us, and the fact that this experience is "artificial". Additionaly, this safety theory assumes it includes the nature of what will exactly happen in the LHC. The natural phenomenon could very well be - and probably is - a sign of some natural equilibrium taking place at levels that no actual theory of the matter can grasp. Getting in touch with new theories and paradigms seems to be the goal of the experience, so they have to be taken into account.

There is an irrational thinking that this experience is safe, relying solely on the illusion of beeing able to fully wrap our minds around the problem.

Personnaly I'm almost sure that any real objective mind would determine there are some big risks.

We are playing with toys we don't understand, for reasons we shouldn't pursue. It is destroying us slowly. We are interfering with some balance and it is getting back to us by ways that we can't imagin. Scientists may be animated by good will, but the experience is pushed by big money.

Who knows what happened with the last experiences / disasters ; Did we create chain reactions that we aren't aware of ? Are they causing some diseases that we didn't yet (or maybe never will) link to it ? The truth is that nobody knows.

Let's not put me in some "religious" or "irrational" or "anti-progress" labelled box. (I'm the same commenter as above, but wanted to separate my personal intuition from the facts).

It was me who wrote this sentence. It isn't a logical fallacy because there doesn't follow any conclusion. I haven't argued for this reason something does or doesn't exist, I have merely pointed out a fact. Make out of it what you want.

Regarding the quote below, there is no logical fallacy, because Hawking radiation is expected based on well understood physical laws applied in a regime that is within the laws's scope of applicability.

That is, Bee and Stefan are not giving a popularity argument, no more than when Boeing expects one of its plane designs to fly when built.

Yes, it is possible to imagine reasons why the plane won't fly, but the consensus that the plane will fly is not based on a poll or popularity contest.

Stefan and Bee, you wrote:

"...Hawking radiation (:)... its existence is expected in almost all theoretical scenarios investigated..."

This unfortunately is a formal logical fallacy (or case of incorrect argumentation) called Appeal to popularity (or, 50 million Frenchmen can't be wrong).

Hence it should not ever have been or be used by CERN or anyone as a plank of a case supporting using the LHC.

Every new technology has risks. Also the LHC. I don't think anybody denies that. I would think the largest risk in this case is a technical failure and severe injury for the people who work there. The concerns that have been raised have been taken very seriously and been investigated. I occasionally find it kind of funny, this idea that the evil particle physicists are so eager to have a new toy that they would destroy the whole world for it. Physicists are human beings like everybody else, and we all want to live safely on this planet for some more while. I also don't want to see any bioengeneer breeding a super rat that lives from human blood and kills half of the world population. I suspect the reason why this sounds to some people more absurd than black holes eating the earth is selective knowledge about either one or the other field, as well as influence by the media. Best,

I haven't really followed on the topic but in case the black hole would swallow a single quark, and acquire a net color they would need to have non-abelian hair. We never really considered this option since we assumed the color charge would be neutralized due to confinement. Either way, I don't think one can reliably say very much about this question without actually having a quantum theory for black holes. Best,

Greg Landsberg [...] chose some very different cross-section as his mini-black-hole scattering rate is < 1 in an iron block the size of the earth-moon distance...

Indeed, his estimate corresponds to a cross-section smaller by a factor 1000, roughly speaking.

In the estimate we have presented here, the 200 km is the average distance between two encounters of the black hole with a nucleon - but it's quite obvious that in most such encounters, nothing will happen at all, and the black hole will just fly straight through the nucleon.

The point is that the nucleon is about 1000 times larger in diameter than the black hole's horizon, and for the black hole, the nucleon is just a quite fluffy cloud of a few partons. This can easily account for a factor 1000 when estimating an actual cross section. Of course, one has to factor in the PDFs, and make some plausible assumptions about black hole-parton cross sections... that's much more complicated then.

As for the high production rate of black holes, well, one should then do an actual calculation for the fate of this stuff, with a consistent use of cross sections...

And than, of course, angular moementum is an important extra ingredient, as Uncle Al has pointed out...

I am well aware of this, and you may have noted that the phase space argument is just a very rough estimate, especially since we didn't say anything about actual transverse momentum distributions.

But the main motivation for the post was to point out some orders of magnitude, and that the phase space for black holes produced in colliders and trapped in the Earth's gravitational field is actually quite small in the first place. That's a far cry from a full-fledged analysis - after all, we have just been using a few numbers and a little algebra...

I imagine that the Mangano-Giddings report will provide all the missing details ;-)

Does someone know when and where it will be published? Is a recent talk by them about this online somewhere?

I wonder if you could comment on this page, specifically the discussion under statements 4 and 5. Would you say that unlike the page author, you have an analysis that proves statement 4 (black holes take too long to eat Earth) at a very high level of confidence?

But more objectively we can say it doesn't imply any safety as there is two key differences here : The distance to us, and the fact that this experience is "artificial".

Well, as has been mentioned quite often already, such collisions happen just above our heads on a regular basis, when high-energy cosmic rays hit the atmosphere. The experiment just tries to make them happen in a way that there is detector around.

The argument that potentially dangerous stuff created in the atmosphere will just zip through the Earth without doing harm because of its high momentum is of course valid, and one has to do an actual calculation including realistic cross sections etc... That has, by the way, also be done before the first nuclear reactions had been started artificially.

Hi anonymous (1),

Can you cite references from peer-reviwed journals for them?

Well, we have just been using some undergrad physics and high-school algebra... as for the kinematics of a collision, you may follow the links to see how rapidity is defined, and the reference for the plot has been given. If you look it up at spires, by clicking on the link that we have provided, you can check out quite easily the complete literature related to to the topic, including the papers on the arxiv and the references of the corresponding peer-reviewed publications.

I wonder if you could comment on this page, specifically the discussion under statements 4 and 5.

You may have noticed that the probability for non-escape velocity given by Landsberg in (5) is the same that follows from the rapidity distribution argument we have used here. As for cross sections mentioned in (4), the back-of-the envelope numbers we have used do not replace a detailed calculation, but they set a reasonable upper (worst-case) limit, I hope.

There should be no doubts here in the comment section, that in some minds that what was "Law versus Law" will have it's participants also "here" wondering as well. Leaving their comments, scientific/intuitively otherwise?:)

Following Giddings work I moved slowly to consider this case as if the conditions would have been presented in the cosmic ray collision scenarios as well. What effect GZK cutoff in the determination, Stefan/Bee?

Other examples of the interplay between accelerator physics and astroparticle physics are provided by the following areas: extra dimensions and mini-black-hole production; neutrino oscillations; electroweak baryogenesis; dark matter consisting of the lightest supersymmetric particle (LSP); magnetic monopole production; and ultra-high-energy cosmic rays (UHECR).

Fig. 2.Image showing how an 8 TeV black hole might look in the ATLAS detector (with the caveat that there are still uncertainties in the theoretical calculations).

"New Physics?" The "crossover point" was of interest to me, and it's effect in contributing to climate change? Other possibilities as well.

I would think if Cern was to think about these conditions, then it would not be to unnatural to consider these issues as well?:) They had answered the perspective of the strangelets? I have it somewhere.

A short quibble - it doesn't really affect your figures - but if you weight the elements composing the earth by the fraction they occur, then the average atomic weight is about 16 and number is about 33.

So the earth is, to first order, entirely made of sulfur!

I sort of figured the BH would be more or less at rest with the initial velocity of CERNs angular speed in the ECI frame, a few hundred kph or so. And the BH would pick up about 100 nucleons or so every trip through the earth and back.

If you weight the elements composing the earth by the fraction they occur, then the average atomic weight is about 16 and number is about 33.

That's true, but then we have to take into account that matter in the Earth's interior has a higher density than at the surface because of pressure. The Earth's mean density is about 5.5 g/cm³ - that's roughly the average of the densities of sulfur (≈ 2 g/cm³ - I don't trust the 5.4 g/cm³ hyperphysics quotes for orthorhombic sulfur) and iron (≈ 8 g/cm&sup3), so I have chosen iron to be on the safe side...

The BH would be more or less at rest with the initial velocity of CERNs angular speed in the ECI frame, a few hundred kph or so.

Actually, not quite - that is an important point. "More or less at rest" is a bit misleading... Just about one black hole out of 100000 has a velocity slower than escape velocity, which is 11 km/s or 25000 mph or 40000 km/h. The overwhelming majority of black holes is much faster than that, easily coming close to the speed of light.

And the BH would pick up about 100 nucleons or so every trip through the earth and back.

It will encounter about 100 nucleons on one trip across the Earth, but this does not mean that it picks up all of them. A nucleon is quite big for the black hole, about 1000 times larger in diameter, and mostly empty. So, in most cases (from the Landsberg estimate quoted earlier, I would guess in 999 out of 1000) it just flies through the nucleon and nothing happens at all...

"Last year, Shaposhnikov and Titarchuk applied their QPO method to three black holes whose masses had been measured by other techniques. In their new paper, they extend their result to seven other black holes, three of which have well-determined masses. "In every case, our measurement agrees with the other methods," says Titarchuk. "We know our technique works because it has passed every test with flying colors."

Photo of the Rossi X-ray Timing Explorer satellite The measurement of the black hole's mass is due to high-precision timing observations made by NASA’s Rossi X-ray Timing Explorer satellite, shown here prior to launch. Credit: NASA> Larger image When Shaposhnikov and Titarchuk applied their method to XTE J1650-500, they calculated a mass of 3.8 Suns, with a margin of uncertainty of only half a Sun. This value is well below the previous black hole record holder with a reliable mass measurement, GRO 1655-40, which tips the scales at about 6.3 Suns."

I guess I worry more about strangelets than black holes. Does anyone here know how the conclusions of CERN's 2003 report are changed when we take into account new developments like the Peng, Wen & Chen paper? Are their kind of negatively charged strangelets ruled out by the moon / cosmic ray evidence? Do we know that there is some combination of coincidences that has to happen multiplying to less than, say, one in a million?

Three models of strangelet production in high-energy heavy-ion collisions have been proposed in the 1980s and 1990s: coalescence [10], thermal statistical production [11], and distillation from a Quark Gluon Plasma (QGP) [12, 13]. The first two models usually predict low strangelet production cross sections at mid-rapidity, as verified by measurements of the related processes of coalescence of nucleons into nuclei [14]. If a QGP is created in heavy ion collisions, it could cool down by distillation (kaon emission) and condense to strange-quark-rich matter in its ground state – a strangelet. However, this requires a net baryon excess and a non-explosive process in the collisions [12, 15]. Neither of these conditions is favored at mid-rapidity in ultra-high energy heavy ion collisions, as suggested by results from the Relativistic Heavy Ion Collider (RHIC) at BNL [16]. Recently a new mechanism for strangelet

The reason I mentioned GZK cutoff was to understand the "energy range that we may be talking about" and the effect it would have on "determination of decay."

I could not help the idea that when the "God particle was introduced" then, we have this history to compare with research that comes along sets our expectation straight. What we know now, exceeds our superstitions. People can get mad at the terms like God particle, strangelets all they want, because it is just an admission of what is not understood, now, becomes a limit to what provides understanding through theoretics and experimentation.

Since Bee and Stefan had talked about quite a bit about GZK I thought it appropriate that from their perspective and work here in Backreaction, they could supply the energy valuations in that energy determination and the values on that decay?

Oh and for further reference to this "Law versus Law" it helps sometimes to understand the basis of these arguments so that what is presented here in this commentary section for questions, enlightens, where one may coming for further questions.

While opening the door to validation of claim in law, it would help then to dissuade whether or not, the arguments of the claim are worth proceeding with?

true, strangelets are an interesting topic on its own! I haven't been following strangelet research lately, so I cannot say much about this right now.

There are all the constraints from the many search programs so far that have not found any strangelets - the last one being that from RHIC. And the argument that they might explain trans-GZK cosmic ray particles because of their peculiar charge/mass ratio has the problem now that the GZK cutoff seems to be real. True, there could be strangelet events in cosmic rays beyond the GZK cutoff, and since the AUGER statistics at the cutoff is not so high so far, it's probably hard to dismiss them from GZK arguments.

Anyway, I didn't know of the paper by Peng, Wen and Chen, thanks for the pointer. But they write that the strangelets they propose have some built-in maximal size that prevents them from growing without bounds: "However, they are unable to transform our planet into a strange star for the following two reasons. First, the positively charged slet-1 is the energy minimum for the same parameters. And secondly, when the electron’s Compton wavelength (≈ 386 fm) is reached, the constraint [... related to the β-equilibrium, see page 2, before equation(7)] is no longer valid, and so the strangelet will be neutralized and ceases to expand its size." (page 4 of hep-ph/0512112). That's about 60 times larger than a lead nucleus, but still small compared to the size of an atom. To my understanding, that means that once they will have reached this maximal size, they are not detectable anymore, and they just "look" like a very massive neutral atom.

Maybe there is also an update around somewhere concerning strangelets, but I don't know.

Thanks, Bee and Stephan, for your replies to my points (those made as Anonymous; these made as LW).

Re the popularity logical fallacy, sorry, I made a mistake.

I have often read elsewhere that “most physicists expect” so in haste I read “expected in almost all theoretical scenarios” as that. I suppose it goes to show we all can make mistakes, and I’ll come back to that.

The case your article makes is only as strong as its weakest link, and in analysing your case, I started (now, obviously, mistakenly – sorry, again) with the popularity fallacy. I now turn to another criticism which can be - and of course has been - made of “expected in almost all theoretical scenarios”. The whole basis of science is the empirical checking out of theoretical scenarios. How can you scientifically justify accepting a risk – especially a very large one - just on a theoretical scenario? And if there are other adequate reasons to accept the risk, under Occam’s Razor, isn’t this argument unnecessary?

I also asked :Can you cite references from peer-reviewed journals for them? and you answered:

"Well, we have just been using some undergrad physics and high-school algebra... as for the kinematics of a collision, you may follow the links to see how rapidity is defined, and the reference for the plot has been given. If you look it up at spires, by clicking on the link that we have provided, you can check out quite easily the complete literature related to to the topic, including the papers on the arxiv and the references of the corresponding peer-reviewed publications.

"More specific references may be found in the CERN Yellow Report "Study of potentially dangerous events during heavy-ion collisions at the LHC: Report of the LHC Safety Study Group".

I was really seeking references to the validity of the case you made as a whole, not its component parts. The parts a claimed revolutionary type of car is made from may be all be good and indeed standard, but it does not mean the car as a whole should not be tested.

Finally, I used my own mistake above as an example that we all can make mistakes. People with a vested interest in something forthcoming and keen therefore for it to go ahead, can overlook things via such mechanisms as optimism bias

http://en.wikipedia.org/wiki/Optimism_bias

and therefore be at risk of mistakes.

This leads me to ask you, as physicists, aren’t you uncomfortable that CERN, accused of running risks with the LHC, is also being the judge via its handpicked Lsag panel of whether there are risks? Can the accused also be the judge? Is there, formally, a risk here?

As for optimism: It seems that you need quite some optimism to expect the production of mini black holes in the first place. After all, their production os based on the still speculative existence of large extra dimension.

In March 2005, at the "40th Rencontres de Moriond", a meeting on "QCD and Hadronic interactions at high energy", physicist Bruce Knuteson did a poll (arXiv:hep-ex/0504041), asking his colleagues where "the first sign of new physics will come from". The results are in his slides for the conference (ptt file) Averaging over the over the responses of several hundred professional physicists, just 21 percent had voted for "Large Extra Dimensons", the prerequisite for black holes. And this does not mean that these signals must be there at the LHC. Lisa Randall, for example, seems to be convinced that black holes are "out of reach of LHC".

To your questions about risk analysis, why should I be uncomfortable? There is no black magic in the risk analysis, and you have to play with open cards: state and justify your assumptions, do the math. That had be done at RHIC in the paper by Jaffe, Busza, Sandweiss and Wilczek, and it will be done in the report of Mangano and Giddings, which is currently under review.

It may be true that this had could be done earlier, but I guess most physicists have thought of it as a complete waste of time because the answer is quite obvious - and I can completely sympathize with that. But you are right, formally, there is a risk, and one should figure out as thoroughly as possible what can be happen before one hits the red button. On the other hand, the accused is obviously not the judge - I guess you are not a scientist, because otherwise you would know that your allegations are quite offensive? - because the rules of physics are not made by CERN.

It's strange to see a lot of discussion about theory when there is compelling experimental evidence (cosmic rays) that we are in no danger.

Suppose we generously assume that a 14 TeV proton-proton collision generates a stable (no hawking radiation) black hole with some non-negligible cross section. Given that a small but non-negligible percentage of these black holes will be below escape velocity, this clearly presents a dangerous situation.

Now, assume that a 14TeV "colliding-beam" collision (not fixed target) is the threshold for black hole production. Given the observed flux of cosmic rays that could produce a fixed-target collision with a relative energy above that which is equivalent to a 14TeV "colliding-beam" collision, the first question is: how many black holes would be produced per year when cosmic rays interact with the earth? Has anyone worked this out?

Assuming that none of these black holes would be below escape velocity, this argument holds no weight. But then the second question would be: assuming the comsic ray flux and energy distribution to be about the same everywhere in the universe, then, given the known density of material in the universe, and a generous interaction cross section (so that we get, say, a few black holes per year below escape velocity at the LHC), what would be the expected number of these stable black holes produced since the big bang? It seems like an order of magnitude calculation could be worked out without too much trouble -- I wonder has anyone done it? I suspect one would find that there would be a tremendous number of black holes floating around, and a large flux through the earth at any given moment!

proton-proton collisions at the LHC with a collision energy of sqrt(s) = 14 TeV correspond to "fixed target" cosic ray protons with an energy of 100000 TeV or 10^17 eV. The flux of cosmic rays of this energy is about 10000 per km² per year, or 200000 per second integrated over the whole surface of the Earth. The LHC will have about 600 millions proton-proton collisions per second, so, that's 3000 times more collisions than are going on at the very same time with the same energy somewhere within the atmosphere.

However, if a mini black hole is produced in such a collision in the atmosphere, it is completely impossible that it is below escape velocity - it will have essentially the speed of light.

But of course, as you say, if these mini black holes did not decay, they would accumulate, and be flying around in the cosmos in quite high numbers. They would, for example, constantly impinge on neutron stars. Since neutron stars are dense lumps of nucleons, the chances would be much bigger that they will stick, and "suck in" the neutron star.

Tommaso has mentioned in his blog that the existence of old neutron stars is an important argument of the Mangano-Giddings paper. It seems that tey have done exactly the estimate that you are suggesting - we will see the details...

stefan said... "However, if a mini black hole is produced in such a collision in the atmosphere, it is completely impossible that it is below escape velocity - it will have essentially the speed of light."

But what if such a black hole has non-zero charge. Wouldn't it react so much that it slows down.

“But what if such a black hole has non-zero charge. Wouldn't it react so much that it slows down.”

Although it has been shown that a black hole can initially have three basic measureable attributes; that being gravity, angular momentum and charge. It has also been demonstrated and reinforced by Hawking, Penrose and others, that unlike gravity and angular momentum which remain, any charge would quickly dissipate from a stable black hole; and so although it might be formed with charge it would probably be lost in a very short time. This of course it not to serve as a professional response as perhaps Stefan may offer; it is solely as I have become to understand it.

Stefan:On the other hand, the accused is obviously not the judge - I guess you are not a scientist, because otherwise you would know that your allegations are quite offensive? - because the rules of physics are not made by CERN.

Just to point back to Stefan's remark to LW for further clarification

•We expect that the report will be submitted for refereeing to a panel of experts, outside CERN and not engaged in the LHC programme

But what if such a black hole has non-zero charge. Wouldn't it react so much that it slows down.

I guess the orders of magnitude involved here are not very evident... now, if a cosmic ray proton hits a nucleus in an atom "at rest" in the atmosphere with an energy such that in the centre of mass of the colliding particles, the energy is the same as the LHC, this centre of mass moves with a gamma factor of 7000, corrresponding to 0.999999991 times the speed of light. If you take a collision with some heavy nucleus found in the atmosphere, say argon, there may be a difference in the last decimal or so. That's what I had in mind with saying "impossible that it is below escape velocity".

I agree, you can construct contrieved cases that a charged mini black hole that neither evaporates nor changes its charge (I don't know if that makes sense) will loose energy by standard Bethe-Bloch and probably gets stopped somewhere in the Earth - but if this happens, it seems to be quite harmless, as the Earth is more than 6000 years old ;-)

I was just pointing out that the "if earthgobbling black holes could be formed in LHC, then earthgobbling black holes would already have been formed by cosmic rays, and since this earthgobbling has evidently not occurred, we conclude that earthgobbling black holes will NOT be formed in LHC" --- argument is still robust. Just consider charged ones.

Remember it's important to discover as many different types of naturally occurring earthgobbling black holes as we can, because we know that we can add them all to our list of hypothetical objects that don't actually exist.

Hi,As Daniel Hanske pointed out in my blog (German) the Schwarzschild radius of these mini black holes would be much smaller than 10^-18m (as stated above), namely ~ 10^-50m when putting in the 14 TeV/c^2 mass.Is there something else to this calculation or did both Mr. Landsberg, you and I oversee some 32 orders of magnitude...?Cheers,Leonard

I have no idea what some Daniel pointed out elsewhere, but I assure you 10^-18 m is (up to a factor of order one) correct. It is simply the inverse of a TeV, for this estimate assumed to be somewhere close by the new fundamental scale. I strongly suspect that the 32 orders of magnitude difference come from the fact that whoever did this calculation might not have realized we are talking about a scenario with large extra dimension (as was mentioned repeatedly), which lowers the Schwarzschild Radius by many oders of magnitude and which is the reason that these black holes can be produced to begin with:

Black Hole production at the LHC could never be the achieved were General Relativity just as we are used to it, and as we have measured it since centuries, because then - you get it - the LHC could never ever get particles close enough together to form a black hole. For details, see e.g. this paper. Best,

sorry if I misunderstood you. Indeed, we are talking about contrived cases ;-), and for some of them, especially the charged ones, the cosmic ray argument effectively defuses the "earthgobbling" disaster scenario.

To come back to your very first question, concerning the possible "cosmic" population of mini black holes and its consequences, it seems that's an important point in the Mangano-Giddings paper. We will see. It has been used before - Sabine mentions it in hep-ph/0412265 and refers e.g. to astro-ph/0205170.

A micro black hole(mBH) with a crossection of 10^-36m that traverses the Earth's diameter, would sweep out a volume of about 10^-29m^3 or about the order of 10 atoms. This would take 0.7 hours for a slow mBH that simply fell through the LHC floor through the centre of the earth to oscillate back and forth with S.H.M. Everything in the the equivalent of those 10 atoms, all the empty space, the electrons, and the quarks, will have been transected. Even taking the typical atom as being sulphur or oxygen or silicon, and not iron(most typical in the core), we are talking an initial accretion rate of around 300 nucleons in 0.7 hours, or over 400 per hour. Even if we reduce the diameter by a factor of ten, this reduces to 4 per hour. This doesn't sound like Greg Landsberg's estimate of around one nucleon per hundred hours.

Re my last post (April 05, 1.41 pm) asking who should decide whether the LHC poses a risk, Stefan commented (April 05, 4.59 pm) in effect that “the rules of physics” will decide. Of course, in turn those rules of physics must be interpreted by people. I was making the point that such people can have biases, conscious or unconscious. Yesterday I found some more words on the issue, and thought I would try to post them, because they are from Backreaction itself (written by Bee). I quote selected sections as follows:http://backreaction.blogspot.com/2006/08/lee-smolins-trouble-with-physics.html

BY BEE ON WEDNESDAY, AUGUST 02, 2006Lee Smolin's Trouble with Physics “I … decided it’s time to post the review on Lee Smolin's new book….“The fourth - and in my opinion most important - part (of the book) then analyzes why and how science works best, what sociological problems we face…“It addresses the problem of groupthink in the string community… “Political pressure on young as well as senior scientists has grown to become a reason for concern.”

A group exhibiting sociological problems and groupthink, and experiencing political pressure (which has) grown to become a reason for concern is hardly a group to give the best decision, I would think, especially if it required the bringing of bad news to senior members of the group.

Further, Lee Smolin in this blog made this comment:http://backreaction.blogspot.com/2006/08/lees-comments.html

“With the scene set, here is my critique. First, to progress, science needs a mix of hill climbers and valley crossers. The balance needed at any one time depends on the problem. The more foundational and risky a problem is the more the balance needs to be shifted towards valley crossers. If the landscape is too rugged, with too many local maximum, and there are too many hill climbers vrs valley crossers, you will end up with a lot of hill climbers camped out on the tops of hills, each group defending their hills, with not enough valley crossers to cross those perilous ridges and swampy valleys to find the real mountain.

“This is what I believe is the situation we are in. And-- and this is the point of Part IV -- we are in it, because science has become professionalized in a way that takes the characteristics of a good hill climber as representative of what is a good, or promising scientist. The valley crossers we need have been excluded, or pushed to the margins where they are not supported or paid much attention to.

“My claim is then…. we need to shift the balance to include more valley crossers.”

I suggest it is those unhappy with how the LHC risk question is being handled by CERN who look more like the valley crossers in this question.

I think you completely misunderstood the point with the valley crossers. This is about finding alternative approaches (different hills), which possibly requires you to go through a low (the valley). I don't see what this has to do with the risk estimate for the LHC. You are of course right that people working on a topic run in danger to have a biased opinion, in the sense that nobody wants to see a shortage for his/her own research topics. It is however highly implausible to me that thousands of physicists would agree on a matter on the risk of causing the end of the world. I do not think that anybody would have to be afraid of his/her job should he have calculated such a risk and published it. Lee's book focuses on a completely different problem, that is the question on judging on the promise of a research project. Either way, a sociological argument like this is a reason to be especially careful, but it can on its own not replace a scientific one. Best,

Hi BeeThanks for your large-minded reply. You wrote:“You are of course right that people working on a topic run in danger to have a biased opinion, in the sense that nobody wants to see a shortage for his/her own research topics. It is however highly implausible to me that thousands of physicists would agree on a matter on the risk of causing the end of the world. I do not think that anybody would have to be afraid of his/her job should he have calculated such a risk and published it.”Encouraging to read this – I hope you’re right!You also wrote:“… a sociological argument like this is a reason to be especially careful, but it can on its own not replace a scientific one.”I completely agree – to be really clear, I reiterate that I was not suggesting that one replace the other, but simply that both needed to be born in mind.

I was just re-reading some of these articles, and there is one point that I find esp. confusing, namely the argument that the black holes at the LHC would be more dangerous than those from cosmic rays because they are less fast. Besides that Stefan explained above very nicely that the typical product of high energy collision has a velocity considerably above the earth's escape velocity, I don't see why these things should be more dangerous. In fact, it is those produced in cosmic rays which had a better possibility to gain mass, exactly because they are faster (higher gamma factor). The reason is that they have to make their way through the earth in a shorter time, which means that the potential mass gain (mass per time) is higher (alternatively, in the Black hole's restframe, the density is higher because of the gamma factor). One can estimate however that even for the black holes produced in cosmic rays this additional factor is not high enough for the black hole to grow (not even in matter as dense as a neutron star) since the mass loss through evaporation is several orders of magnitude larger. For those created at the LHC the mass loss would be even more dominant.

5.CERN says: "THE COLLISIONS HAVE LESS ENERGY THAN A FEW FLYING MOSQUITOS, so must be safe."False analogy. The energy of the neutrons (mosquitos) that triggered the exponential process (E=mc2) in the TRINITY ATOM BOMB TEST 1945 in the New Mexico Desert was many orders of magnitude less than this, but STARTED AN EXPONENTIALLY INCREASING PROCESS (E=mc2)...During the short time the U235 is explosively brought to a supercritical state (E=mc2), EVEN ONE SLOW NEUTRON (mosquito) causing (E=mc2)fission is sufficient.

It's not the 'M A S S' (mosquito) involved, it's; the 'C A T A L Y T I C' (E=mc2) effect of these sub-atomic explosions at dangerously high energy levels, not 'just' the effect on the particles themselves.

Thanks for posting such a comprehensive reasoning and scientific explanation for this "black-hole creation" problem. This is an explanation that a layman can understand. I have NO knowledge of particle physics. I'd be a Luddite in terms of physics ability. But this knowledge "a black hole has to have significant mass to do damage". In otherwords unless the gravitational pull of the micro-blackhole exceeds that of the mass that it is trying to swallow, then you won't have a problem. :| At least that's what I'm getting here.

I have common knowledge about physics, aka I really would have no idea what I'm talking about as far as proofs go. But.. talking as a human being, I find it HIGHLY unethical to proceed with a project that has so much worry in the public's eye. Granted, media inflates these dangers too outrageous proportions, there should be much more assurance that there is no cause for concern. The project management should be able to come out to the public with confidence and tell the whole world themselves what they are doing, the concerns of dangers, and in simple terms why there is no cause for concern. The first I heard about this was from a random person in a random chat room, and after scouring MANY websites to find solid evidence, I mostly found documentation that sounded more speculative than factual, and was not very concise and definite in their explanations.

In short, just imagine how many people have heard about this and have worried their brains out over it. From a statistics standpoint, there is never 100% confidence in anything, but they need to at least say they are personally confident that it will not cause harm and say WHY they are so confident. The way it sounds to me, their confidence lies somewhere between 1% and 99.999% for dangerous scenarios. Anybody would worry over a 1:50,000,000 chance of the earth being wiped out, its how the general public works (look at lottery..)

I've been reading the postings on this page, and many others on the internet, and having trouble getting my head around the logic that supporters of LHC have used. Analysis of risk is typically made in direct proportion to the size of risk, and it typically involves a sense of personal choice. For example, I choose to fly on airplanes. There is generally a one in 15 million chance of being in a plane crash. I take that risk because a.) I'm willing to personally take it, and b.) the potential risk (the plane crashing and killing me and everyone else onboard) is relatively low (in comparison, let's say, to say the entire planet getting squashed). If someone gave me a button, and said "go ahead, push it, there's a one in 15 million chance the earth will explode", would I do it? No. If someone said that the same button had a 14,999,999 in 15,000,000 chance of solving all the problems of mankind plus a 1 in 15 million chance of the world exploding, would I push it? Maybe. I understand I'm rambling, but the point is quite simple - risk versus reward, plus the element of personal choice. The risk for the LHC is low, but the effect if an error were to occur is too high. The payoff is -- though great -- too low to justify the risk. And there is no personal choice in this risk for the vast majority of people living on the earth -- including, by the way, the 1 billion some-odd people that live in poverty and don't have access to even basic needs, like clean water. The billions of dollars that were spent on LHC would have been better spent helping those people. Am I missing something?

The question you are asking is a good one, I've asked it myself here. It is a huge political question. There certainly has to be a balance between driving progress in the richer countries and helping progress in the less rich countries, and where it is is a matter of discussion and will likely remain one for a long time.

However, this is not the question here. The LHC is build, and the question is now, do we turn it on or what?

You are barking up completely the wrong tree. Who you should blame for scaring the public are money-hungry news-reporters who have no qualms publishing irresponsible stories about catastrophe scenarios that have no scientific backup whatsoever without ever clarifying that what they are writing is pure fantasy. If you blame that on science and ask, based upon such behavior, to stop doing it, that's pretty much the end of progress altogether. There is something very very very wrong with the media in the United States and unfortunately this is starting to swap over to the other side of the ocean. What is wrong with it is very easy to see. There is no feedback mechanism that gives incentives for quality. Operation for profit cares only about whether a story sells. If the buyer doesn't care about quality that whole system drifts away into cheap and content free infotainment. There is no way you can build informed decision making or a working polical system on a public influenced by such crap, not to mention science literacy.

So. That's then what your 'free market' gives you and where the 'invisible hand' leads you. Instead of blaming physicists for that crap, you should blame a failure in the political system that - in my opinion - is based on a bad education of how democracy works and what politics is good for.

“The billions of dollars that were spent on LHC would have been better spent helping those people. Am I missing something?”

This is one of the most overused and wrong headed reasons for not doing something which is so often brought up. The problems that the people you mention never were to any large extent created by some sort of conspired unbalanced distribution of wealth, yet rather the lack of a plan to create wealth in the areas of the world you mention.

The real solutions are many and complex that begin first with the ridding of ignorance facilitated by the promotion of education. After this the many layers of problems can be addressed, with solutions like the creation and access to public resources, fostering political stability and with it the creation of an economy that is sustainable and growing.

This is not simply a matter of investment, yet more so planning, proper management and most importantly a sense of urgency and willingness of the people so affected to change. Oh yes, strangely enough the unwarranted fear that people have regarding the LHC has it’s root cause as being the same, which is ignorance, which can only be dispelled by education and the willingness to learn.

The bottom line here is that the risk involved of the LHC is many orders of magnitude lower then your airplane crash and yet it is most certain to create new knowledge and with it wealth.

“If you give a man a fish he will have a single meal. If you teach him how to fish, he will eat all his life.

"This is one of the most overused and wrong headed reasons for not doing something which is so often brought up. The problems that the people you mention never were to any large extent created by some sort of conspired unbalanced distribution of wealth, yet rather the lack of a plan to create wealth in the areas of the world you mention.

The real solutions are many and complex that begin first with the ridding of ignorance facilitated by the promotion of education. After this the many layers of problems can be addressed, with solutions like the creation and access to public resources, fostering political stability and with it the creation of an economy that is sustainable and growing. "

But to get those real solutions going is going to take money. So why not put the money in that direction instead of in building bigger and bigger dumb particle colliders? It doesn't matter if the colliders don't have any risk -- the fact still remains that the money could do better if more were put in the direction of the many real and complicated solutions you mentioned. In that direction of developing and implementing plans to get more education, more stability, etc. How is a particle masher going to help with _those_ problems? You do not seem to have understood the point. The point has nothing to do with some perceived risk of the collider blowing up the Earth, it has to do with the wisdom of the spending. Plenty of unwise spendings have been done that have NOT blown up the Earth.

And "sustainable and growing"? Earth is a finite planet, it cannot "grow" forever and yet still be "sustainable".

It is my understanding that although many black holes might be produced in the LHC, they will generally be so small they will immediately evaporate (and/or escape the earth's gravitational field). I read somewhere that a stable black hole would have to weigh on the order of 10 micrograms. Is that a number you would agree with?

If so, that would mean that the particles involved in the collision would have to have a relativistic mass of at least that, probably much more.

Can you describe the collisions in the LHC in those terms? I realize it is a very elementary question, but you two are the best source I have found for LHC questions.

In my opinion, the biggest danger would be that some reactions would occur undetected and would keep happening over an unknown duration. For example, until somewhat recently neutrino's were a theoretical particle until a method was discovered (based upon the assumption that they did exist) to detect them.

The very nature of the tests that will be performed at the LHC defines that the results will not necessarily be anticipated and therefore a substantial number of methods cannot be established to detect them as they initially occur.

That being the case some and possibly many reactions will take place with unknown results. It may be that nothing more than small amounts of energy are released or it may be that significantly larger amounts of energy are released causing damage to the equipment.

I just hope that something useful comes out of such an expensive and highly anticipated experiment. It could simply end up being a "dud".

the obvious problem to me is not wether or not the LHC will destroy the earth via a spew of mini stable black holes eating the earth from within (which IS albeit VERY VERY unlikely, a possibility) but if the LHC provides militaries new toys to play with. How about a single bomb that can wipe out europe and leave no trace of radiation? Science doesn't exsist in a vacuum as much as scientists wish it did. What does this achieve/promise? what are the benefits to mankind outside of proving hawking or m-theory right or wrong? Hadrons are responsible for gravity, right?, so isn't the apple proof enough?

aside from that, most of the physists calculate schwarzfield radiation decay of ONE mini black hole, which is, a force of nature that is beyond our understanding of time and space, despite the best guesses in the standard model or particle physics / without a ToE. BUT what if 1000 are made and merge? what if anti-matter/matter combo is poofed out of nothing and from that feeds it on a chain recation scale. Would it not irradiate all life on earth? Have all the possibilities been thought out OUTSIDE of some myopic physics equation? Sadly i must say to these arrogant 'smart people' - good luck, we're ALL gonna need it.

if a black hole acquires a quark every 400 miles of journey and hawking radiation is a pipe dream, the black hole will grow, correct? if one such black hole is created per second, how long will it take a black hole or a collection of black holes to acquire enough mass to swallow a planet. i suspect that the answer isn't infinity. if it's greater than five billion years, then we will have more serious problems to confront before the crust of the earth begins to drop out from under our feet. i have read recently that the odds have been adjusted upward for the creation of black holes at the lhc and ran across this blog while looking for that story. can anyone point me to such an updated story?

Robert: There is no updated story, if anything the number of expected black holes has been falling with more accurate studies, and Hawking radiation is not a pipe dream. You seem to have misunderstood almost everything I write. There is no consistent theory WITHOUT Hawking radiation. If anything, then the absence of Hawking radiation is a 'pipe dream'.

This is great information! Thank you for writing it; now I'm not scared to go to sleep at night. I was afraid the LHC would create black holes that would swallow the earth. Your explanation helped me understand there probably won't be many black holes, and if there are, they'll either shoot off into space or disintegrate. Thank you! --Jonathan, age 8 (typed by his mom)

I read your post and the relevant comments with some apprehension. A stated above, only 1 in 100,000 mini black holes created is expected to have a velocity less than escape velocity. Using other date from the blog, this equates to an expectation of one black hole which will be captured by earth’s gravity being produced every 28 operational hours.

You inform us that members of this significant subset will “typically” have an escape velocity in some other direction. In short, the escape velocity theory that is laid out here is the antithesis of reassuring. In fact some simple math suggests that to the extent that we rely on the mini black holes escaping earth’s gravity before they destroy us all, we are deluding ourselves.

Given the above here appears to be only two hopes for our survival. Either we are all wrong, and no mini black holes will be produced, or; Hawking radiation will be rapid enough to cause the demise of the phenomenon before it can swallow a nucleon or another mini black hole.

The statement that “there is no theory to describe what happens when a tiny black hole encounters a nucleon” should give us all pause as a black hole without escape velocity will encounter a nucleon, on average, after traveling only 200 kilometers. One percent of such tiny black holes will encounter a nucleon after traveling only 2 kilometers.

Let me ask a rhetorical question: given the theoretical and experimentally unverified nature of all of this, how many of us would make the following wager with a gun to our children’s heads. If the experiment confirms hawking radiation theory as presently configured the gun is removed; but if the experiment produces data which requires a reanalysis or reconfiguration of the theory of hawking radiation, as presently configured, the trigger will be pulled.

No one with any knowledge of the history f scientific progress and development would take that wager. Yet that is exactly what we are doing right now.

Proposal: lets turn this thing on for a second and then turn it off. Turning it on again after we have had an opportunity to analyze all of the data produced. Lets confirm Hawking’s theory in a way which will minimize the chance of destroying everything.

Although better judgment tells me that indeed the majority is correct in concluding that our civilization will probably not be destroyed by an artificial black hole, logic dictates that creating one must be possible. It is given that black holes exist, and it is also given that all existing black holes were produced at some point in the past. We can identify the naturally occuring 'device' which produces black holes: supernovae explosions originating from hypermassive stars. If we could 'build' a cloud of gas large enough to collapse into such a star and had the patience enough to wait, it might be said that we had the means to 'manufacture' a black hole. Such an arrangement is obviously quite logistically impossible for us. Yet because of the existence of even one such natural configuration which produces a black hole, it follows that it must be possible, however technologically demanding, to re-create such conditions artificially. Some 'device' built by man COULD artificially produce black holes, although whether the LHC is one such device remains to be seen. Another topic discussed was the presence of cosmic rays amongst old stars as evidence against black hole formation. I think i have heard somewhere that such an event in which two cosmic particles collide at such an angle and velocity as to cause a black hole is rare. So rare, in fact, that if it has ever occured at all in the universe's history, the chances of one such nicro-hole floating into your vicinity of the cosmos are practically nil. Yet I am without calculations to corroborate this anecdotal probabilistic conjecture.However, if we accept that a black hole producing arrangement is possible, then we accept that LHC may possibly inadvertently be one. As this seems to me to be accurate, then it would appear that we are indeed risking our own destruction in the pursuit of knowledge whose usefulness is uncertain at best.On the other hand, perhaps it's worth the risk. But I'll need to e promised a warpdrive, transporters, and maybe a few phasers. Beam me up!